【6】Principal component analysis of electricity use in office buildings

www.elsevier.com/locate/enbuild

Principalcomponentanalysisofelectricityuseinofficebuildings

JosephC.Lama,*,KevinK.W.Wana,K.L.Cheunga,LiuYangbaBuildingEnergyResearchGroup,DepartmentofBuildingandConstruction,CityUniversityof,

TatCheeAvenue,Kowloon,SAR,China

bSchoolofArchitecture,Xi’anUniversityofArchitectureandTechnology,Shaanxi710055,China

Received10May2007;receivedinrevisedform2June2007;accepted5June2007

Abstract

Principalcomponentanalysiswasconductedonfivemajorclimaticvariables—dry-bulbtemperature,wet-bulbtemperature,globalsolarradiation,clearnessindexandwindspeed.Twenty-eightyear(1996–2000)long-termmeasuredweatherdatawereconsidered.Atwo-componentsolutionwasobtained,whichcouldexplain80%ofthevarianceintheoriginalweatherdata.Monthlyelectricityconsumptiondatarecordedduringa5-yearperiod(1979–2006)weregatheredfrom20fullyair-conditionedofficebuildingswithcentralisedHVACsystemsinsubtropical.Electricityuseperunitgrossfloorarearangedfrom163to3kWh/m2.Theseconsumptiondatawerecorrelatedwiththecorrespondingprincipalcomponentsusinglinearmultipleregressiontechniques.Thecoefficientofdetermination(R2)variedfrom0.76to0.95indicatingreasonablystrongcorrelation.Itwasfoundthattheregressionmodelsdevelopedcouldgiveareasonablygoodindication(mostlywithin3%)oftheannualelectricityuse,butthemonthlyestimatesmightdifferfromtheactualconsumptionbyupto9%.Attemptwasalsomadetodevelopageneralregressionmodelforthe20buildings,whichhadanR2of0.84withamaximummean-biasederrorof18.6%andamaximumroot-mean-squareerrorof21.4%.

#2007ElsevierB.V.Allrightsreserved.

Keywords:Principalcomponentanalysis;Officebuildings;Energyuse;Subtropical

1.Introduction

Energyisakeyelementintheoveralleffortstoachievesustainabledevelopment.In,thereisagrowingconcernaboutenergyconsumptioninbuildings,especiallynon-domesticbuildings,anditsimplicationsfortheenviron-ment.Abouttwo-thirdsoftheimportedprimaryenergyrequirement(mainlycoal,oilandnaturalgas)wasusedforelectricitygeneration.Electricityuseinbuildingsisthusakeyenergyend-user.Recently,themuchpublicisedreportbytheInter-governmentalPanelonClimateChange(IPCC)hashelpedgeneratealotofinterestsinhavingabetterunderstandingoftheenergyusecharacteristicsoffullyair-conditionedofficebuildingsin,especiallytheircorrelationswiththeprevailingweatherconditions.Therehadbeenanumberofstudiesonenergysignaturesofbuildingsforenergysavingsanalysisofpre-andpost-buildingretrofitsusingmeanoutdoortemperaturesordegree-daysdata[1–4].Earlier

worksoncooling-dominatedofficebuildingsinsubtropicalalsoconcentratedlargelyonthemeanmonthlyoutdoordry-bulbtemperatureanddegree-daysdatausingsimpletwo-parameterregressionanalysistechniques[5–7].Whiletheseempiricalorregression-basedmodelsshowgoodcorrelationsbetweenenergyuseandtheprevailingweatherconditions,mostofthemeitherconsideronlyoneweathervariable(dry-bulbtemperature),ordonotadequatelyremovethebiasintheweathervariablesduringthemultiplelinearregressionanalysis[8].Theprimaryaimofthepresentworkistoinvestigatetheseasonalvariationsinelectricityuseincooling-dominatedofficebuildingsinsubtropicalclimatesasafunctionoffivemajorweathervariablesdirectlyaffectingbuildingperformance–dry-bulbtemperature,wet-bulbtemperature,globalsoarradiation,clearnessindexandwindspeed–usingprincipalcomponentanalysis.

2.Selectionofbuildingsandelectricityconsumptiondatagathering

Atotalof20purpose-builtofficebuildingswereselectedforthisstudy.Theselectionwasbasedonthefollowingcriteria:

*Correspondingauthor.Tel.:+85227887606;fax:+85227887612.E-mailaddress:bcexem@cityu.edu.hk(J.C.Lam).

0378-7788/$–seefrontmatter#2007ElsevierB.V.Allrightsreserved.doi:10.1016/j.enbuild.2007.06.001

J.C.Lametal./EnergyandBuildings40(2008)828–836829

(a)Thesampleshouldincludethetwomajorbuildingenvelopedesignsin,namelyreinforcedconcretewithinsertedwindowsandcurtainwalls.

(b)Thesampleshouldincludethethreemajorglazingtypes,namelyclear,tintedandreflectiveglass.

(c)Allbuildingsshouldhavecentralisedheating,ventilationandair-conditioning(HVAC)systems.

(d)Mostimportantofall,availabilityofmonthlyelectricityconsumptiondataforatleast5years.The20officebuildingsselectedwerebasedonourearlierwork—sixonIsland,nineintheKowloonPeninsulaandtheremainingfiveintheNewTerritories[7].Inordertoretaintheindividualbuildinganonymity,theyarereferredtoasBuilding1,Building2,andsoon.Informationonthebuildingdesignsandthebuildingservicesinstallationwasobtainedfromtheoriginaldesignandcontractdocumentwhereverpossible.Additionaldatawereobtainedthroughsitevisits,discussionswiththearchitects,engineersandbuildingmanagementpersonnel.Table1showsasummaryofthekeybuildingdataandinformationonthebuildingenvelopedesigns.Thegrossfloorarea(GFA)rangesfrom1287m2(Building9)to98197m2(Building4)andthenumberofstoreysfrom6to48.Mostofthemwerecompletedduring1980stoearly1990s,the‘‘booming’’periodofthelocaleconomyingeneralandtheconstructionindustryinparticular.Ingeneral,therearetwomajorbuildingenvelopedesigns,namelycurtainwallsandreinforcedconcretewithinsertedwindows.Buildingscom-pletedinthe1980sandearly1990stendtohavecurtainwalldesigns.Areaofthewindowsvariesagreatdeal;thelowestwindow-to-wallratio(WWR)is0.27inBuilding9andthehighest0.65inBuilding4.Withatypicalfloor-to-floorheightof3.4m,theserepresentwindowheightsofabout0.9and

Table1

SummaryofbuildingenvelopeinformationBuildingnumber12345671011121314151617181920

a2.2m,respectively.Buildingsconstructedinthe1960sand1970stendtohavesmallerwindowswithsingleclearglazing(shadingcoefficient0.9),whereasthosedesignedmorerecentlyappeartohavelargerwindowswithtinted(shadingcoefficient0.5–0.65)orreflective(shadingcoefficient0.25–0.45)glass.Insubtropical(latitude=22.38N),solaraltitudeoftenexceeds608duringhotsummerdays,resultinginsubstantialsolarheatabsorptionbythehorizontalroof.Asaresult,theusualpracticeistohavethermalinsulation(usually50mm)totheroofslabwithacommonU-valuerangeof0.4–0.5W/m2K.Theroofstructureismassive,usuallynolessthan300mmthickconsistingofrooftiles,waterproofingasphalt,cementandsandscreed,thermalinsulation(usuallyexpandedpolystyrene),reinforcedconcreteplusthefinalindoorfinishofatleast10mmgypsumplasterandalayerofenamelpaint.Togetsomeideaaboutthebuildingshapesandforms,theoverallbuildinglayoutswereobtained.Theyarelargelysquare,rectangularorcombinationofboth.Intermsoftheimpactsofbuildingshapesonheatingandcoolingloads,rectangularbuildingshapesalongtheeast–westdirection,ingeneral,wouldhavemaximumenergysavinginallclimates;whereaselongatedbuildingsonthenorth-southaxiswouldincreasetheoperatingcostsbecauseofhighersummerpeakcoolingloadsandhigherwinterheatingloads.Inthisstudy,about40%oftheofficebuildingsareintheeast–westdirection,andtheremaining60%indifferentorientations.

Withthemonthlyenergyusedataandcorrespondingbuildingdesignandoperationinformation,differentenergyusecharacteristicsandpatternscanbeestablished.Intheinvestigationandevaluationofbuildingenergyuse,differentcategoriesofloadsshouldbeconsidered.Thefirstcategoryisthebaseload,whichisdefinedasthenon-weather-relatedenergyuse.Typicalexamplesareartificiallighting,office

GFA(m2)17,40024,23730,74498,1978,31612,6363,60412,1181,28760,96191,80012,6109,76529,72211,6106,1507,12933,85223,10744,0

Numberofstorey142514481120715748673212610261121

EnvelopetypeaRCCWCWCWRCRCRCRCRCCWCWRCRCCWRCRCRCRCRCCW

Shadingcoefficient0.900.400.500.250.900.900.900.650.900.250.250.900.900.450.900.900.900.550.600.65

WWR

U-Values(W/m2K)Wall

Window5..85.63.45.65.65.65.65.63.63.45.65.65.65.65.65.65.65.65.6

Roof0.50.50.50.40.50.50.50.50.50.40.40.50.50.40.50.50.50.40.50.5

OTTV(W/m2)28.333.322.834.032.733.833.533.028.033.234.024.627.423.833.337.027.031.022.021.0

Shape

coefficient(mÀ1)0.190.150.110.090.160.130.240.170.280.100.090.090.200.120.240.220.180.150.200.10

Internalloaddensity(W/m2)336362404039383350514432434040484141

0.500.500.450.650.450.400.290.360.270.500.450.390.460.450.320.310.370.330.400.351.91.41.91.91.91.41.41.41.41.91.91.91.91.91.41.41.41.91.91.9

CW,curtainwalls;RC,reinforcedconcretewithinsertedwindows.

830J.C.Lametal./EnergyandBuildings40(2008)828–836

Fig.1.Annualelectricityuseperunitgrossfloorarea.

equipment,otherelectricalappliancesandtheverticaltransportation(i.e.liftsandescalators).Thesecondcategoryisenergyconsumedintheheating,ventilationandair-conditioningplantsandsystems.Thisisweather-sensitiveandrequiresthedeterminationofhowmuchenergyisusedforheatingandcooling(bothlatentandsensible)andelectricityusefortheassociatedequipmentsuchasfansandpumps.Officebuildingsinhaveatypicaloperatingscheduleof10-h(08:00–18:00)workingday,and51/2-dayweek.Atotalof5-year(1996–2000)electricityconsumptiondatawerecol-lectedandanalysed.Inallthebuildings,totalelectricityconsumptionvariedslightlyfrom1yeartoanother,duemainlytotheslightlydifferentweatherconditionsandmoreimportantlytothevariationsinbuildinguseandoperations,especiallyoccasionalovertimework.Therewasnoclearpatternindicatinganyspecificvariationfromany1yeartoanother,andtheaveragepercentagedifferencewasjustover3%.Togetanideaabouttheorderofmagnitudeoftheelectricityuseamongthe20buildings,annualconsumptiondatawerecompared.The5-yearaveragedannualelectricityconsumptionvariedagreatdeal,from0.22MWhinBuilding9to36.9MWhinBuilding4,duemainlytothebuildingsizeand,toalesserextent,thedifferencesindesignsandoperations.Toaccountforthedifferencesinbuildingsize,theaveragedannual

Fig.2.Monthlymeandailyelectricityuseinthe20buildings.

J.C.Lametal./EnergyandBuildings40(2008)828–836831

electricityusedataforeachbuildingweredividedbythecorrespondingGFAtogivetheenergyutilisationindex(EUI),alsoknownasnormalisedperformanceindicator(NPI),whichisusedtocomparetheenergyuseintensityamongdifferentbuildings.Fig.1showstheEUIsforthe20buildings,whichvariedfrom163kWh/m2inBuilding13to3kWh/m2inBuilding3,withameanconsumptionof270kWh/m2.ThedifferenceinEUIisduemainlytothevariationsinlightingandequipmentloaddensity,demandsforverticaltransportationandbuildingoperations.Togetanideaabouttheseasonalvariations,asummaryofthemonthlyaveragedailyelectricityconsumptioninthe20buildingsisshowninFig.2.Ingeneral,all20buildingshadshowndistinctseasonalvariationswithpeakconsumptionoccurringbetweenAprilandNovember,the8-monthcoolingseasonforcooling-dominatedofficebuildingsinsubtropical.

3.Principalcomponentanalysisoflong-termweatherdata

Principalcomponentanalysis(PCA)isamultivariatestatisticaltechniquewhichcanhelpgetabetterunderstandingofthedependenciesexistingamongasetofinter-correlatedvariables[9,10].PCAisconductedoncentreddataoranomalies,andisusedtoidentifypatternsofsimultaneousvariations.Itspurposeistoreduceadatasetcontainingalargenumberofinter-correlatedvariablestoadatasetcontainingfewerhypotheticalanduncorrelatedcomponents,whichneverthelessrepresentalargefractionofthevariabilitycontainedintheoriginaldata.Thesecomponentsaresimplylinearcombinationsoftheoriginalvariableswithcoefficientsgivenbytheeigenvector.Apropertyofthecomponentsisthateachcontributestothetotalexplainedvarianceoftheoriginalvariables.Theanalysisschemerequiresthatthecomponentcontributionsoccurindescendingorderofmagnitude,suchthatthelargestamountofvarianceofthefirstcomponentexplainsthelargestamountofvarianceoftheoriginalvariables,thesecondthenextlargest,andsoon.

Atotaloffiveclimaticvariableswereconsidered,namelydry-bulbtemperature(DBT,in8C),wet-bulbtemperature(WBT,in8C),globalsolarradiation(GSR,inMJ/m2),clearnessindex(Kt,dimensionless)andwindspeed(WSP,inm/s).DBTaffectsthethermalresponseofabuildingandtheamountof

Table2

Coefficientsofthefiveprinciplecomponentsandrelevantstatistics

heatgain/lossthroughitsenvelopeandhenceenergyuseforthecorrespondingsensiblecooling/heatingrequirements,whereasWBTdictatestheamountofhumidificationrequiredduringdrywinterdaysandlatentcoolingunderhumidsummerconditions.Informationonsolarradiationiscrucialtocoolingloaddeterminationandthecorrespondingdesignandanalysisofair-conditioningsystems,especiallyintropicalandsub-tropicalclimateswheresolarheatgainthroughfenestrationsisoftenthelargestcomponentofthebuildingenvelopecoolingload[11].Inadditiontoglobalsolarradiation,Kthelpsidentifytheprevailingskyconditions.Winddata,intermsofspeedandprevailingdirectionduringdifferentseasons,areimportantinnaturalventilationdesignandanalysis.Thesedatawouldalso,tosomeextent,affecttheexternalsurfaceresistanceandhenceU-valuesofthebuildingenvelope[12].Thelongertheperiodofrecordsandthemorerecenttheweatherdataare,themorerepresentativetheanalysiswillbe(sinceshorterperiodsmayexhibitvariationsfromthelong-termaverageandconsideringonlyveryearlyperiodofdatamaynotreflectthepresentweathercondition).Twenty-eight-yearlong-term(1979–2006)weatherdatafromthelocalobservatoryweregatheredfortheanalysis.Tokeeptheanalysismanageable,onlydailyvalues(atotalof10,227Â5data)wereconsideredinthePCA.Table2showsasummaryofthecoefficientsofthefiveprincipalcomponentsandtherelevantstatisticsfromthePCA.Theeigenvalueisameasureofthevarianceaccountedforbythecorrespondingprincipalcomponent.Thefirstandlargesteigenvalueaccountsformostofthevariance,andthesecondthesecondlargestamountsofvariance,andsoon.Thepercentageisgivenbytheratiooftheindividualeigenvaluetothetraceofthecorrelationmatrix,andcalculationofallpossibleeigenvalues(i.e.consideringallprincipalcomponents)wouldaccountforallofthevarianceoftheoriginalvariables.Principalcomponentscanberankedaccordingtotheirabilitytoexplainvarianceintheoriginaldataset.Acommonapproachistoselectonlythosewitheigenvaluesequaltoorgreaterthanone(eigenvaluesgreaterthanoneimpliesthatthenewprincipalcomponentscontainatleastasmuchinformationasanyoneoftheoriginalclimaticvariables[13])orwithatleast80%cumulativeexplainedvariance[14].Inthisstudy,aprincipalcomponentwasconsideredtobesignificantiftheeigenvaluewasgreaterthanoneorthecumulativeexplainedvariancereached80%.Itcanbeseenthatthefirsttwoprincipal

Principlecomponentcoefficient1

Climaticvariable

Dry-bulbtemperatureWet-bulbtemperatureGlobalsolarradiationClearnessindexWindspeed

Eigenvalue

Explainedvariance

Cumulativeexplainedvariance

0.8510.7630.8550.678À0.1692.5350.550.5

20.5160.639À0.480À0.7080.2131.4529.179.6

3À0.024À0.0380.1320.1470.9620.9719.398.9

40.050À0.007À0.1460.1290.0010.040.9.7

5À0.0840.086À0.0120.024À0.0010.020.3100.0

Relevantstatistics

832J.C.Lametal./EnergyandBuildings40(2008)828–836

Fig.3.MonthlyvariationsinthetwoprincipalcomponentsZ1andZ2.

componentshaveeigenvaluesgreaterthanonewithacumulativeexplainedvarianceof80%(i.e.thistwo-componentsolutionaccountsfor80%ofthevarianceintheoriginalclimaticvariables).Thesetwoprincipalcomponentswere,therefore,retained.Anewsetofdailyvariables(Z1andZ2)foreachofthetwosignificantprincipalcomponentswasthencalculatedaslinearcombinationsoftheoriginalfiveclimaticvariablesasfollows:

Z1¼0:851ÂDBTþ0:763ÂWBTþ0:855ÂGSRþ0:678ÂKtÀ0:169ÂWSPZ2¼0:516ÂDBTþ0:639ÂWBTÀ0:48ÂGSRÀ0:708ÂKtþ0:213ÂWSP

(2)

4.Correlationbetweenelectricityuseandprincipalcomponents

Seasonalvariationsshownbythetwoprincipalcomponents(Fig.3)andmonthlyaveragedailyelectricityconsumptionamongthe20buildings(Fig.2)areverysimilar.Attemptsweremadetocorrelatetheconsumption(E)withthetwoprincipalcomponents(Z1andZ2)usingmultipleregressiontechniqueasfollows:

EðkWh=dayÞ¼aþb1ÂZ1þb2ÂZ2

(3)

(1)

MeasureddataforthefiveclimaticvariableswereanalysedandthedailyvaluesofZ1andZ2determinedusingEqs.(1)and(2).Fig.3showsthemonthlyaveragedailyvaluesofthetwoprincipalcomponentsforthe5-yearperiod(1996–2000).DistinctseasonalvariationscanbeobservedinbothmonthlyprofilesshowingpeakelectricityconsumptionduringthecoolingseasonfromApriltoNovember.ItisinterestingtonotethatthevaluesofZ1areabouttwoandahalftimesZ2.

Table3showsasummaryoftheregressioncoefficientsandthecoefficientsofdetermination(R2).ItcanbeseenthatR2variesfrom0.763inBuilding4to0.945inBuilding15withasamplemeanof0.865,andthecorrelationsareconsideredstrong.Threebuildings(Buildings7,8and15)havenegativeintersectionswhenZ1andZ2arezero(i.e.negativecoefficient‘‘a’’).Toassesshowwellthelinearregressionequationscouldpredictthemonthlyelectricityuse,themean-biaserror(MBE)andtheroot-mean-squareerror(RMSE)weredeterminedasfollows:

P12

ðxiÀyiÞ

MBE¼i¼1(4)

12

J.C.Lametal./EnergyandBuildings40(2008)828–836

Table3

Summaryofregressionanalysisforthe20buildingsBuildingnumber

a

b1b2R2MBEkWh/day

12345671011121314151617181920

1,6527,99756958,2557961,022À1,091À701915,74234,2243,067996,077À94746379916,6272,7449,335

712004856818610450112872755635816255174143311

17219445855811925814792299159822191465283277323149

0.8050.8170.9320.7630.8260.7970.9130.9100.90.8290.8560.8520.8780.8880.9450.9120.9100.8430.9030.824

157.7À537.5À676.815.4À394.0À422.350.9À168.921.3À319.01081.257.467.6807.4À2.0À110.4129.2À511.3À321.8À390.9

(%)1.9À2.5À2.11.9À7.3À5.22.2À2.13.7À0.61.50.51.63.1À2.7À2.52.7À1.7À2.0À1.4

RMSEkWh/day495.81234.11927.33637.3461.6707.6196.7591.0.23022.63438.0778.4394.01497.3609.3235.7337.51004.9627.01693.4

833

(%)6.15.75.93.78.58.88.67.27.15..87.49.35.76.25.37.03.33.96.2

wherexiisthepredictedmonthlyelectricityconsumption(kWh/day),yiisactualmonthlyelectricityconsumptionrecorded(kWh/day)

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP122

i¼1ðxiÀyiÞ(5)RMSE¼

12Themean-biaserrorprovidesinformationonthelong-termperformanceofthemodelledregressionequation.ApositiveMBEindicatesthatthepredictedannualelectricityconsump-tionishigherthantheactualconsumptionandviceversa,andtheRMSEisameasureofhowclosethepredictedmonthlyprofileistotheactualonebasedonthemonthlyelectricitybills.Itisworthnotingthatoverestimationinanindividualobservationcanbeoffsetbyunderestimationinaseparateobservation.Electricityconsumptiondatarecordedduringtheyear2000wereusedfortheerroranalysis.TheMBEandRMSEdeterminedforthe20buildingsarealsoshowninTable3.ItcanbeseenthattheMBEvariesfrom7.3%underestimationinBuilding5to3.7%overestimationinBuilding9,andtheRMSEfrom3.3%inBuilding18to9.3%inBuilding13.Thissuggeststhattheregressionmodelsforindividualbuildingscangiveagoodindicationoftheannualelectricityuse(mostlywithin3%),butthemonthlyestimatesmaydifferfromtheactualconsumptionbyupto9%.Toascertainanyunderlyinglong-termeffect,similarregressionanalysiswasconductedusing5-yearaverageconsumptiondata.Thecorrelationstrengthwassignificantlyincreased—R2rangingfrom0.8inBuilding6to0.995inBuilding15withameanof0.951,whichishigherthanthemeanR2of0.925foundinourearlierworkontwo-parameterregressionusingcoolingdegree-daysstatistics[7].

Thenon-weather-independentandweather-dependentcom-ponentsoftheelectricityconsumptionareaffectedbythedesignofthebuildinganditsbuildingservicesinstallations.Itwasfoundthattheinternalload(i.e.lightingandequipment)andbuildingenvelopeload(i.e.heatgainthroughthewalls,windowsandroofs)showedgoodcorrelationswiththenon-weather-independentandweather-dependentcomponents,respectively.Inanattempttodevelopageneralregressionequationforofficebuildingsinsubtropical,monthlyelectricityconsumptiondataforthe20buildingswereregressedagainstthecorrespondinginternalloaddensity,buildingenvelopeloadandthetwoprincipalcomponents.Toaccountforthevariationsinbuildingscale/size,monthlyelectricityuseperunitgrossfloorareawasused.TheinternalloaddensitydataweretakenfromthoseshowninTable1.Togetanideaaboutthecoolingloadsandhenceenergyuseduetobuildingenvelopeheatgain,theoverallthermaltransfervalue(OTTV)foreachbuildingwasdetermined.OTTVisameasureoftheamountofheatgainthroughthebuildingenvelope[15,16].Sincemostbuildingsarehigh-rise(10-storeyormore),externalwallareaismuchbiggerthantheroofarea.Furthermore,alltheroofsinthesampledonothaveskylightandhencenosolarheatgainwhichisthedominantcomponentinthetotalbuildingenvelopecoolingloadinsubtropical.Thisleadstocomparativelysmallconductionheatgainthroughtheroof.Therefore,onlywallOTTVwasconsideredandasummaryisshowninTable1.ItcanbeseenthatOTTVrangedfrom21W/m2inBuilding20to37W/m2inBuilding16withanaveragevalueof29.7W/m2.Thismeansthatonaveragetherewas29.7Wofheattransferredintothebuildingthroughthebuildingenvelope(wall)perunitbuildingenvelopearea.

Variationsinbuildingshapecombinationwillgreatlyaffecttheamountofexternalsurfaceareaforagivenvolumeenclosed.Forinstance,atallbutnarrowbuildingwillhaveahighsurfaceareatovolumeratio.Thisiscalledtheshape

834J.C.Lametal./EnergyandBuildings40(2008)828–836

coefficient,Cf,definedasthetotalsurfaceareaofthebuildingenvelope(wallsandroof)tothespacevolumeofabuildinginsidetheenvelope[17].Atallnarrowbuildinghasasmallroofandisaffectedlessbythesolargainonthefacadesurfacesduringthesummermonths.Ontheotherhand,tallbuildingsarenormallysubjectedtohigherwindvelocityandthusgreaterinfiltrationrateofheatgainandheatloss.Asummaryoftheshapecoefficientsforthe20buildingsisshowninTable1.Asmallshapecoefficientindicatesalargebuildingandviceversa.Itcanbeseenthattheshapecoefficientvariedfrom0.09to0.28,withameanvalueof0.16.Toagoodapproximation,heatgainthroughthebuildingenvelopeperunitgrossfloorareawasobtainedasfollows:Hb¼OTTVÂCfÂhf

(6)

whereHbisbuildingenvelopeheatgainperunitfloorarea(W/m2),OTTVisoverallÀ1thermaltransfervalue(W/m2),Cfisshapecoefficient(m)andhfisthefloor-to-floorheight(m).Withatypicalfloor-to-floorheightof3.4m,themonthlymeandailyelectricityuseperGFAdataforthe20buildingswereregressedagainsttheinternalloaddensity,buildingenvelopeheatgain(Hb),andthetwoprincipalcomponents.Thefollowinggeneralregressionequationforofficebuildingswasobtained:

E0¼À0:766þ0:0205ÂILDþ0:0009ÂHbþ0:00ÂZ1

þ0:0091ÂZ2

(7)

whereE0ismonthlyelectricityuseperunitgrossfloorarea2perday(kWh/m22day),ILDisinternalloaddensity(W/m).TheRoftheregressionequationis0.841,indicatingreasonablystrongcorrelationsbetweenthemonthlyelectricityuseandthefourindependentvariables.Toassesstheperformanceofthegeneralregressionmodel,Eq.(7)wasusedtopredictthemonthlyelectricityconsumptionusingZ1andZ2valuesfromyear2000forthe20buildingsandcomparedwithelectricityuserecordedinyear2000.AsummaryoftheMBEandRMSEisshowninTable4.TheMBErangesfromanunderestimationof0.125kWh/m2perdayinBuilding14toanoverestimationof0.098kWh/m2perdayinBuilding11,andtheRMSEfrom0.029kWh/m2perdayinBuilding19to0.14kWh/m2perdayinBuilding3.Asapercentageoftherespectivemeasuredmeanmonthlyelectricityconsumption,MBEvariesfromÀ14.2%inBuilding14to18.6%inBuilding9,andRMSEfrom4.1%inBuilding19to21.4%inBuilding9.Itappearsthat,beinglow-rise(onlysix-storey)withthesmallestGFAandthelowestinternalloaddensity,Building9tendstohavethelargestpercentageMBEandRMSE.Thissuggeststhatthegeneralregressionmodeltendstobeweightedtowardsthelargerhigh-risebuildingswithhigherinternalloadsamongthebuildingsample.ItisinterestingtonotethatwhileindividualbuildingR2wasgreatlyimprovedbyusing5-yearaveragedataforcorrelationbetweenelectricityuseandthetwoprincipalcomponents(meanR2increasesfrom0.865to0.951),thereisonlymarginalincreaseinR2forthegeneralregressionmodel(from0.841to0.8).

Table4

SummaryofMBEandRMSEforthe20buildingsusinggeneralregressionmodel(Eq.(7))Buildingnumber

MBERMSE(kWh/m2day)

(%)(kWh/m2day)(%)10.05010.70.07516.120.0505.60.0707.83À0.042À3.60.14012.040.0979.70.10510.450.0091.40.0375.760.0203.20.0538.370.0121.90.08513.38À0.055À8.10.07210.690.08218.60.09521.410À0.034À3.80.0626.9110.09812.50.10913.912À0.096À11.50.11313.7130.06314.40.08419.414À0.125À14.20.13415.215À0.113À13.40.13816.316À0.0À7.50.0659.117À0.020À2.90.0466.918À0.081À9.00.09610.619À0.013À1.80.0294.120

0.056

9.1

0.082

13.4

Anattemptwasmadetocorrelatethemonthlyelectricityusedirectlywiththeinternalloaddensity,buildingenvelopeheatgain(Hb)andthefiveclimaticvariables.TheR2ofthiseight-parameterregressionmodelwasfoundtobe0.844,slightlyhigherthanthe0.841forthefive-parameterregressionmodel(i.e.Eq.(7)).WebelievetheprincipalcomponentanalysisapproachismoreappropriatethanthedirectmultipleregressionofthefiveclimaticvariablesbecausePCAcanindicatethesimultaneousvariationsandtherelativeimportanceoftheclimaticvariablesinrepresentingtheprevailingdaily/monthlyweatherconditions.

5.Discussionandconclusions

Electricityuseof20fullyair-conditionedofficebuildingsinsubtropicalwasanalysed.Theconsumptionpatternsshoweddistinctseasonalvariations,indicatingsub-stantialincreasesintheelectricaldemandsduringthecoolingseasonfromApriltoNovember.Basedonthe5-year(1996–2000)averagedmonthlyelectricityusedata,theannualelectricityuseperunitgrossfloorareawasfoundtorangefrom163to3kWh/m2,withanaverageof270kWh/m2.ThedifferenceinelectricityuseperunitGFAwasduemainlytovariationsinthelightingandequipmentloaddensity,demandsforverticaltransportation(i.e.liftsandescalators)andoperatinghours.

Principalcomponentanalysisoftheprevailingweatherconditionswasconducted.Fivemajorclimaticvariables–dry-bulbtemperature,wet-bulbtemperature,globalsolarradiation,clearnessindexandwindspeed–wereconsidered.Itwasfoundthatatwo-componentsolutionwouldcontainasmuchinformationastheoriginalfivevariablesandcouldexplain80%ofthecorrespondingvariance.Thetwoprincipal

J.C.Lametal./EnergyandBuildings40(2008)828–836835

componentsexhibitedseasonalvariationssimilartothemonthlyelectricityconsumptionrecorded.Three-parameterregressionmodelsweredevelopedtocorrelatethemonthlyelectricityuseandthecorrespondingprincipalcomponentsdataforeachofthe20buildings.Thecoefficientofdeterminant(R2)rangedfrom0.763to0.945withameanof0.865,indicatingstrongcorrelation.Itwasfoundthattheregressionmodelsforindividualbuildingscouldgiveareasonablygoodindication(mostlywithin3%)oftheannualelectricityuse,butthemonthlyestimatesmightdifferfromtheactualconsumptionbyupto9%.Comparedwithconventionaltwo-parameterregressionmodelusingdegree-daysdata,regressionmodelsinvolvingprincipalcomponentanalysistendtoshowstrongercorrelationandhenceprovidebetterestimatesofseasonalvariationsinelectricityuseinair-conditionedofficebuildinginsubtropicalclimates.

Examiningthecrosscorrelationbetweendifferentbuildings,itwasfoundthatthecoefficientsinthethree-parameterregressionequationsforindividualbuildingswerecloselyrelatedtothebuildingenvelopeandbuildingservicesdesignsintermsofbuildingenvelopeheatgainandinternalloaddensity.Attemptwasmadetodevelopageneralregressionmodelforthe20officebuildings.ThemonthlymeandailyelectricityuseperGFAwasexpressedintermsoffourindependentvariables,namelyinternalloaddensity,buildingenvelopeheatgainandthetwoprincipalcomponents,withanR2of0.841.Themean-biasederrorrangedfromanunderestimationof0.125kWh/m2perdayinBuilding14toanoverestimationof0.098kWh/m2perdayinBuilding11,representing,respectively,À14.2and12.5%ofthecorrespondingmeanmonthlyelectricityconsumptionrecorded.Theroot-mean-squareerrorvariedfrom0.029kWh/m2perday(4.1%)inBuilding19to0.14kWh/m2perday(12%)inBuilding3.Itseemedthat,beinglow-rise(onlysix-storey)withthesmallestGFAandthelowestinternalloaddensity,Building9tendedtohavethelargestpercentageMBEandRMSE.Thissuggeststhatthegeneralregressionmodeltendstobeweightedtowardsthelargerhigh-risebuildingswithbiggerinternalloadsamongthebuildingsample.

Itisbelievedthatforindividualbuildings,monthlyandhenceannualelectricityusecanbewellrepresentedbylinearregressionmodelsinvolvingprincipalcomponentanalysis.Theprincipalcomponentanalysisdevelopedcanbeusedasatoolforweathernormalisationand/orinter-yearcomparisons.Thiscouldhavepracticalapplications.First,energyuseindifferentyearscanbeadjustedforvariationsintheweatherconditionsandcomparedtoidentifyanyunusualincrease/decreaseinenergyuseaspartofamonthly/annualenergyauditandmanagementprogramme.Second,thiscouldbeusedtodetermineenergysavingsresultingfrombuildingandbuildingservicesinstallationretrofits.

Amoregeneralregressionmodelforair-conditionedofficebuildingsinsubtropicalclimates,however,wouldprobablynotbeabletogiveverygoodestimatesoftheenergyuseduetodiversityinthebuildingandbuildingservicesdesignsaswellastheactualoperations.Thiscouldpossiblybeovercomebyhavingsub-categoriesaccordingtotheprevailingmajor

buildingdesigntypesandmodesofbuildingoperations.Ofcourse,muchlargerbuildingsamples(farmorethanthe20buildingsconsideredinthisstudy)areneeded.Giventhegrowingconcernsaboutclimatechangeanditsimpactonenergyuseinthebuiltenvironment,ageneralregressionmodelforofficebuildingscouldhaveimportantapplicationsbecauseitcouldbeusedtoassessthelikelychangesinenergyuseintheentireofficebuildingsectorusingpredictions(i.e.daily/monthclimaticdata)fromvariousgeneralcirculationmodelsbasedondifferentIntergovernmentalPanelonClimateChange(IPCC)emissionscenarios.Moreworkssuchasenergyauditsandsurveysoflargerbuildingsamplesandanalysisofpredictedclimaticdatafromthemeteorologicalcommunityarerequired.Acknowledgements

TheworkdescribedinthispaperwasfullysupportedbyagrantfromCityUniversityof(ProjectNo.7002024).K.K.W.issupportedbyaCityUniversityofStudentship.WeatherdatawereobtainedfromtheObservatoryoftheSAR.Theauthorswouldliketothankthetechniciansfortheirhelpwiththegatheringofthebuildingdataandelectricityconsumption.References

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